A digital watermark is a marker embedded in a noise-tolerant carrier signal corresponding to audio, video, or image data. The digital watermark may be used to identify ownership of a copyright of content corresponding to the carrier signal. “Watermarking” is the process of hiding digital information (e.g., the watermark) in the carrier signal. The hidden information may or may not contain a relation to the carrier signal. Digital watermarks may be used to verify the authenticity or integrity of the carrier signal or to show the identity of owners of the underlying content. It is used, for example, for tracing copyright infringements and for banknote authentication.